saturn’s f ring core: calm in the midst of...
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Saturn’s F Ring Core: Calm in the midst of chaos
Part 2
J. Cuzzi, E. Marouf, R. C. French, and R. Jacobson
Saturn’s F Ring Core: Calm in the midst of chaos
Part 2
J. Cuzzi, E. Marouf, R. C. French, and R. Jacobson
How can this be, in the face of pervasive orbital chaos??
The F ring core is very narrow (<1km from occultations; Marouf et al 1986; 2011a,b),
It contains numerous sizeable embedded objects (Murray et al 2008, Esposito et al 2008, Beurle et al 2010),
and it has maintained a very stable orbit over decades (Bosh+2002, Marouf+2011a,b, Albers+2012, Cooper+2012).
Radius relative to mean elliptical orbit
360o of orbit longitude
Orbital chaos is pervasive (Scargle et al 1993, Winter et al 2007, 2010)
Δa (km)
“…all particles in core region are chaotic”; most
extreme case shown.
ISS continues to have trouble tracking objects
(Cooper et al 2006)
Pr Pa
Log
Res
onan
ce s
treng
th
F Ring region is filled by closely spaced resonances
130000 135000 140000 145000 150000
140500 140000 141000
years years 0 20 9.5 10.5
1st 2nd
140221
F Ring core region
a arms
Cuzzi, Whizin, Hogan, Dobrovolskis, Dones, Showalter, Colwell, Scargle 2014
Δa=10m
Prom-F differential prec period
90km
F Ring core (140221: Albers, Cooper)
Cuzzi et al 2014
ti
Showalter & Burns 1982 20
-20 km
Close/eccentric encounters change semimajor axis and synodic period.
Subsequent encounters generally lead to chaotic diffusion of a -
unless canceled immediately, on next encounter after Psyn. We call orbits where this occurs “antiresonances”.
Merge (e, ) of particle and perturber
Δa ~ few km
Perturbation by Prometheus impulses
antialignment
Cuzzi et al 2014
time t t + (m±1/2)Ps
If , cancellation at antiresonance when Stable locations are halfway between resonances
Simple case
time t t + (m±1/2)Ps
If , cancellation at antiresonance when Stable locations are halfway between resonances
Simple case
Actual case time t t + mPs
Now we obtain cancellation when
And because , get “antiresonances” where ,
That is, at or near resonances, not halfway between them Cuzzi et al 2014
-180 -90 0 90 180
Δa
0,2,4,… 1,3,5,…
(35 yrs) Insets adapted from Beurle et al 2010
This works fine when perturbations are weak, in sinusoidal limit, and can be canceled by encounters differing by 180 deg in longitude
-180 -90 0 90 180
Δa
0,2,4,… 1,3,5,…
Δa
:
-180 -90 0 90 180
Δa
0,2,4,… 1,3,5,…
Δa
:
To preserve the long-term stability possible at AR’s, particles can never encounter Prometheus when it is near its apoapse………..
Suggests that corotational resonance acts to select/maintain long-term stable longitudes wrt Prometheus.
Goldreich et al 1986 Porco 1991
Neptune’s arcs are confined by torques in a 2m-fold CIR (inclination type; m=86, due to the very low eccentricity of Galatea), with energy input from the Galatea m=43 ILR. For Prometheus, the CER (eccentricity type) dominates.
Pa
OLR CER
AR 109:108
0.08 km
Resonance locations near the F Ring
Log
torq
ue
RSS sees a different F Ring core Marouf et al. 2011 a,b
RSS core ~0.1-1km wide, vs ISS/UVIS/VIMS “core” tens of km
Comparable optical depth at K, X, S bands (> few cm radius)
Not always detected! (15 of 49 in 2011; 24 of 67 to date)
Esposito et al 2008
1986
Are the RSS occultations consistent with CR idea?
• Start with inertial longitudes of 23 Cassini RSS detections, VGR1 RSS detection, and 43 Cassini RSS nondetections. No discrimination by optical depth of detection.
• Regress to some epoch on comb of candidate mean motions for m=110 CER, varying nPr in fractional steps of 5E-7 (0.07km), and then fold resulting longitudes mod (360/110)o.
• Look for clustering in a restricted range of folded longitudes near (regressed and folded) Prometheus periapse and away from its apoapse. Use Jacobson’s avg. value for Prometheus apse precession, starting with longitude of Cooper et al (2012).
F03
n1
n2
Panels show regressed and folded
longitudes of RSS detections
assuming F Ring Core
at m=110 CER, by stepping Prometheus mean motion
in steps of Δn/n=5E-7
peri apo
F03
n1
n2
peri apo
Panels show regressed and folded
longitudes of RSS detections
assuming F Ring Core
at m=110 CER, by stepping Prometheus mean motion
in steps of Δn/n=5E-7
Uncertainty and variability in Prometheus’ orbit
n
a
Open circles: RSS nondetections
apo peri
ARs and CERs are always very close to OLRs - within 1km across the entire region
CERs always inside OLRs, asymptotically overlapping; ARs sometimes inside, sometimes outside
Hard to tell from SMA-residuals which is actually responsible for stable zones (“stalactites”).
However, there is only one place where the AR and CER exactly coincide. . . . . .
Relative offset between (ARs, CERs) and OLRs
…..exactly where the F Ring core lies (140222.4km)!
It cannot be a coincidence that the F Ring core lies in the only place in the entire F Ring region where the AR and the CER exactly coincide.
Most likely, both AR and CER are required for long term stability.
Relative offset between (ARs, CERs) and OLRs
Summary
F Ring core must be able to track these small modifications to the orbit of Prometheus in order to maintain long-term stability. Stable sites act as “attractors” for wayward particles, perhaps allowing this to happen.
F Ring stability is due to a combination of “antiresonance” (AR) associated with Prometheus’ m=109 OLR, and its m=110 CER. AR is the result of rapid precession of Prom apse, and the long synodic period between Prometheus and an F Ring particle.
F Ring SMA = 140222.4 +/- 0.1 km from 2005-2013 at least; however, it must “breathe” over time as Prometheus orbit varies.
Some dramatic change in Prometheus’ (and Pandora’s) orbits in early 2013 has disturbed the pattern of stable sites. Stable sites may be concentrated in three longitudinal segments.
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